The binary logistic regression model: In [p / (1–p) = a + ∑bixi; where p is the probability of a student achieving 24 or more competencies or do well in the test.
For both, a is the constant, bi values are estimated regression coefficients and xi are the predicting variables. For more details about there models see Menard (1995), Hosmer and Lemeshow (1989) and Gujarati (1988).
In both the cases, a step-wise approach was followed to select the most economic model. This considered only the factors significantly predicting the dependent variables. The non-selected variables were excluded from the final models.
Exploration of school level variation
The ordinary least square regression analysis reveals that of the 27 explanatory variables considered in the analysis, the final model granted only five of them. These include quality of teachers as assessed by the area managers, proportion of contents of the textbooks taught in the classrooms, proportion of Muslims in the schools, teachers’ length of service and number of programme organizers supervised in grade V. Table 32 provides results from the regression analysis.
Regarding predicting the average achievement of the schools, the most important variable was quality of the teachers assessed by the area managers. Schools with better teachers performed well. A positive relationship between schools’ average performance and quality of teacher4 was emerged when influences of other variables were kept constant. The proportion of contents of the textbooks taught in the classrooms has emerged as the second most important predictor. As much as the teachers covered the contents of the textbooks the pupils were more likely to do well in the test. The third important predictor was the proportion of Muslim students in the schools. Increase of the proportion of Muslim students in the schools also increased the average performance of the pupils. The fourth important predictor in this regard was the length of experience of the teachers. The students of the schools were more likely to do well in the test as the duration of experience of teachers increased.
Number of programme organizers supervised the schools during grade V came out as the fifth important predictor of schools’ average achievement. However, a negative relationship was found. If the POs were not changed frequently they were able to supervise schools for longer period which resulted in an increased performance of the schools. These five variables collectively explained 26% of the total variation in the average performance of the schools.
4 See Annex 73 for details of assessing quality of teachers and proportion of contents taught (textbook coverage index)
Table 32. Multivariate regression model predicting mean number of competencies achieved by schools
Explanatory variables Regression
coefficient Beta
coefficient Level of significance Quality of teachers 1.50 0.38 p<0.001
Coverage of textbooks 0.19 0.18 p<0.001
% of Muslim students in schools 0.03 0.15 p<0.01
Teachers service length 0.09 0.12 p<0.05
Number of PO in grade V -0.46 -0.11 p<0.05
Constant 10.66 p<0.001
Adjusted R2 0.26
Analysis of Variance (F value) 20.60 p<0.001 Exploration of student level variation
The binary logistic regression analysis predicting students’ performance considered 16 of the 27 variables in the final model. The explanatory variables in terms of their importance (as per contribution in explaining variation in the dependent variable) are mentioned below.
• Quality of teachers
• Proportion of contents taught
• Religion of student
• Number of school visit by area manager
• Length of service of area manager
• Number of programme organizers visited schools in grade V
• Level of education of programme organizers
• Mothers’ education
• Proportion of girls in school
• Length of service of teachers
• Sex of student
• Having private tutor
• Teachers’ marital status
• Number of school under the programme organizers
• Teachers’ level of education
• Sex of programme organizers
Detail of the analysis is provided in Table 33.
Table 33. Binary logistic regression model predicting competencies achievement of the students
Explanatory variables Regression
coefficient Odds
ratio 95% CI of
odds ratio Level of significance Quality of teacher 0.818 2.27 2.08–2.47 p<0.001 Proportion of contents taught 0.083 1.09 1.06–1.11 p<0.001 Religion of student 0.693 2.00 1.59–2.51 p<0.001 Number of school visit by AM 0.035 1.04 1.02–1.05 p<0.001 AMs length of service 0.096 1.10 1.07–1.14 p<0.001 Number of PO in grade V -0.274 0.76 0.70–0.83 p<0.001 Education of PO 0.087 1.09 1.05–1.13 p<0.001 Mothers education 0.055 1.06 1.03–1.08 p<0.001 Percentage of girls in school 0.023 1.02 1.01–1.03 p<0.001 Teachers length of experience 0.029 1.03 1.01–1.05 p<0.001 Sex of student 0.223 1.25 1.11–1.41 p<0.001 Having private tutor 0.216 1.24 1.09–1.42 p<0.01 Teachers marital status 0.205 1.23 1.06–1.42 p<0.01 Number of school under a PO -0.008 0.99 0.99–1.00 p<0.01 Teachers education -0.059 0.94 0.90–0.98 p<0.01 Sex of PO 0.180 1.20 1.04–1.38 p<0.01 Constant -8.067
Cox & Snell R2 0.14
Nagelkerke R2 0.18
The analysis reveals that the boys, Muslim students and those who had private tutors performed well compared respectively to the girls, non-Muslim students and those did not avail private tutors (Table 33). Schools with married teachers and those supervised by female programme organizers (PO) did well compared to their respective counterparts. Number of change in the position of PO and the number of schools under a PO negatively influenced learning achievement of the students. This means that if the POs were changed frequently or a PO was given responsibility of many schools resulted poor performance of the students. Teachers’ education (measured in terms of years of schooling) also showed negative relationship with students’ competency achievement. All other variables mentioned above had positive influence on learning achievement.
It may be mentioned here that all five explanatory variables appeared in the model predicting school level variation also appeared in the model for predicting student level variation. This indicates importance of these variables in predicting students’
achievement of competencies in BRAC non-formal primary schools. Again, the first three variables in both the models are the same. These are quality of teachers, proportion of contents taught and religion of the students. Note that all types of variables such as students’ background, and characteristics of the teachers, POs and area managers were included in the model as predictors of students’ learning achievement.
Further regression: We have three levels of variables in hand; these are students’
characteristics at household level, schools’ and teachers’ characteristics at school level, and POs’ and AMs’ characteristics at the area level. An attempt was made to see which group of variables explains more in order to predict students’ achievement in the test. Thus, three more regression models were built with the three sets of variables mentioned above. Similar to the above, logistic regression analysis was done for all the three cases.
Five of the eight household level variables came out as the significant predictors of competency achievement of the students (Table 34). These are sex of the students, mothers’ education, provision of private tutor, religion, and availability of electricity at home. The religion came out as the most important predictor of students’
achievement followed respectively by mother’s education, provision of private tutor, availability of electricity at home, and sex of student. All the five variables together explained only 3% of the total variation in the dependent variable.
Table 34. Logistic regression analysis predicting students’ performance against their background variables as predictors
Explanatory variables Regression
coefficient Odds
ratio 95% CI of
odds ratio Level of significance Religion 0.707 2.03 1.64 – 2.50 p<0.001 Mothers education 0.044 1.05 1.02 – 1.07 p<0.001 Private tutoring 0.255 1.29 1.14 – 1.46 p<0.001 Electricity availability at home 0.162 1.18 1.05 – 1.32 p<0.01 Sex of student 0.121 1.13 1.01 – 1.26 p<0.05
Constant -0.733 p<0.001
-2 log likelihood 7973.351
Cox & Snell R2 0.02
Nagelkerke R2 0.03
Of the 10 school level variables (including teacher characteristics) six appeared as the significant predictors of students’ performance in competency test (Table 35).
These are quality of teacher, textbook coverage, proportion of girls in class, teachers’
length of experience, marital status and level of education, and class size. Teachers’
quality assessed by the AMs and proportion of contents taught were the two most important predictors which together explained major part of the total variation in the dependent variable. The independent variables of this model collectively explained 14% of the total variation in the learning achievement of the students.
Table 35. Logistic regression analysis predicting students’ performance against school and teacher centric variables as predictors Explanatory variables Regression
coefficient Odds
ratio 95% CI of
odds ratio Level of significance Quality of teacher 0.800 2.23 2.05 – 2.42 p<0.001 Textbook coverage 0.094 1.10 1.08 – 1.12 p<0.001 Proportion of girls in class 0.026 1.03 1.02 – 1.04 p<0.001 Teachers length of experience 0.029 1.03 1.01 – 1.05 p<0.001 Teachers marital status 0.257 1.29 1.12 – 1.49 p<0.001 Teachers education -0.050 0.95 0.91 – 0.99 p<0.05 Class size 0.027 1.03 1.01 – 1.05 p<0.05
Constant -7.343 p<0.001
-2 log likelihood 7290.849
Cox & Snell R2 0.10
Nagelkerke R2 0.14
Among the 10 variables related to the school supervisors (i.e., PO and AM) six appeared in the model as significant predictors of students’ performance in the competency test (Table 36). These are (chronologically as they appeared in the model) length of service of AM, number of school visit by AM, number of PO in grade V, education of PO, sex of PO and length of service of PO. These variables collectively explained 4% of the total variation in the performance of the students.
Table 36. Logistic regression analysis predicting students’ performance against supervisors’ characteristics and supervision of the schools Explanatory variables Regression
coefficient Odds
ratio 95% CI of
odds ratio Level of significance Sex of PO 0.213 1.24 1.09 – 1.41 p<0.001 Education of PO 0.136 1.15 1.10 – 1.20 p<0.001 POs length of experience 0.022 1.02 1.01 – 1.04 p<0.05 Number of PO in grade V -0.276 0.76 0.70 – 0.82 p<0.001 AMs length of service 0.114 1.12 1.09 – 1.15 p<0.001 Number of school visit by AM 0.039 1.04 1.03 – 1.05 p<0.001
Constant -2.267 p<0.001
-2 log likelihood 7915.780
Cox & Snell R2 0.03
Nagelkerke R2 0.04
From the above-mentioned three models it is clear that the school level variables have more contribution than others in predicting learning achievement of the pupils in BRAC non-formal primary schools and the contribution of the household level variables was the least.
BRAC versus government schools
In an earlier chapter we have seen that BRAC non-formal primary school students in rural areas outperformed their counterparts in nearby government primary schools.
This part of analysis intends to see how far the students of BRAC non-formal schools performed better compared to those in the government primary schools controlling the affects of other variables contributing students’ learning achievement. Data generated in 2008 Education Watch were used in this analysis. As majority of the BRAC non-formal schools are located in the rural areas only the rural schools (both BRAC and government) were considered in this analysis.
Due to the same reason mention in an earlier analysis the number of competencies achieved by the students were divided into two – cutting them through the median value. In this case, the median value was 20. Thus, students achieving 20 or more competencies were considered as well performing students and those achieving less than this were considered as not so well performing students. Such a categorization made it suitable for a binomial logistic regression analysis. The mathematical expression of the regression model is as follows:
In [p / (1 – p) = a + ∑bixi
Where p is the probability of a student achieving 20 or more competencies or do well in the test, a is the constant, bi values are estimated regression coefficients and xi are the predicting variables.
Number of explanatory variables considered in the analysis was 20, which can be categorized into three, viz., students’ socioeconomic background, school-related factors and additional educational inputs. The variables and their measurements are provided in Annex 75. Here too, a step-wise approach was followed to select the appropriate regression model. This considered only the variables significantly predicting the dependent variable. Insignificant variables were excluded from the final model.
Of the 20 variables granted for analysis the final regression model considered eight of them. These include (according to chronology of appearance in the model) private tutoring, fathers education, school type, ethnicity, SMC meeting, teachers’ length of experience, sex and age of student. Table 37 shows the results from regression analysis. Although duration of students availing private tuition and fathers’ length of schooling came out as two most important contributing factors of students learning achievement, the place of school type appeared as the third most important predictor. The finding reveals that BRAC non-formal school students were 4.37 times more likely to do well in the test compared to those in the government schools when the affects of other variables were controlled. The Bangali students did well compared to the ethnic minority students and the boys outperformed the girls.
Positive influences of SMC meeting and teachers length of experience were also observed. However, age of the students affected negatively; indicating relatively younger students performed well in the test. All these eight variables collectively explained 23% of the total variation in the dependent variable.
Table 37. Binary logistic regression analysis predicting performance of BRAC and government schools students
Explanatory variables Regression
coefficient Odds
ratio 95% CI of
odds ratio Level of significance Private tutoring 0.097 1.10 1.07 – 1.14 p<0.001 Fathers’ education 0.089 1.09 1.06 – 1.13 p<0.001 School type 1.474 4.37 1.82 – 6.75 p<0.001 Ethnicity 2.869 17.62 5.17 – 60.01 p<0.001 SMC meeting 0.116 1.12 1.07 – 1.18 p<0.001 Teachers’ experience 0.037 1.04 1.02 – 1.06 p<0.001 Sex of student 0.471 1.60 1.24 – 2.07 p<0.001 Age of student -0.212 0.81 0.72 – 0.91 p<0.001 Constant -3.039
-2 log likelihood 1438.475
Cox & Snell R2 0.17
Nagelkerke R2 0.23
Let us now calculate probabilities of students doing well in the competency test against some of their specific characteristics. This will help understand magnitude of difference between the students of BRAC non-formal primary schools and the government schools in rural areas. In specifying the characteristics of the students we choose the Bangalis because of their majority in the sample and the mean values of other explanatory variables appeared in the model provided in Table 37. Thus, the probabilities were calculated for the Bangali students with age 11.3 years, received 4.5 months of private tuition in grade V, having fathers with 5.1 years of schooling, teachers with 12.6 years of experience and SMC met 8.4 times in a year. The calculated probability of performing well of a BRAC non-formal primary school student with above characteristics was 0.87 if it was a boy and 0.81 if it was a girl (Figure 6). These were respectively 0.61 and 0.49 for the boys and girls of government primary schools with the same characteristics. In other words, a rural boy with the above characteristics receiving education from BRAC non-formal school rather than government primary school increased the probability of performing well in the test by 0.26 (0.61 to 0.87) which was 0.32 (0.49 to 0.81) for the rural girls.
Gender difference was more in government primary schools than BRAC non-formal primary schools.
Figure 6. Estimated probabilities of students performing well in competencies achievement test
0.87 0.81
0.61
0.49
0 0.2 0.4 0.6 0.8 1
BRAC boys BRAC girls Government boys Government girls
Note: These probabilities are calculated from the regression coefficients presented in Table 37 by using the following equation: p = exp(a + ∑bixi) / [1 + exp(a + ∑bixi)]